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  2. Potential flow - Wikipedia

    en.wikipedia.org/wiki/Potential_flow

    Thus the flow occurs along the lines of constant ψ and at right angles to the lines of constant φ. [11] Δψ = 0 is also satisfied, this relation being equivalent to ∇ × v = 0. So the flow is irrotational. The automatic condition ⁠ ∂ 2 Ψ / ∂x ∂y ⁠ = ⁠ ∂ 2 Ψ / ∂y ∂x ⁠ then gives the incompressibility constraint ∇ ...

  3. Vortex - Wikipedia

    en.wikipedia.org/wiki/Vortex

    Within that region, the flow is no longer irrotational: the vorticity becomes non-zero, with direction roughly parallel to the vortex axis. The Rankine vortex is a model that assumes a rigid-body rotational flow where r is less than a fixed distance r 0, and irrotational flow outside that core regions.

  4. Vorticity - Wikipedia

    en.wikipedia.org/wiki/Vorticity

    Parallel flow with shear Irrotational vortex v ∝ ⁠ 1 / r ⁠ where v is the velocity of the flow, r is the distance to the center of the vortex and ∝ indicates proportionality. Absolute velocities around the highlighted point: Relative velocities (magnified) around the highlighted point Vorticity ≠ 0 Vorticity ≠ 0 Vorticity = 0

  5. Potential flow around a circular cylinder - Wikipedia

    en.wikipedia.org/wiki/Potential_flow_around_a...

    In mathematics, potential flow around a circular cylinder is a classical solution for the flow of an inviscid, incompressible fluid around a cylinder that is transverse to the flow. Far from the cylinder, the flow is unidirectional and uniform. The flow has no vorticity and thus the velocity field is irrotational and can be modeled as a ...

  6. Laplace equation for irrotational flow - Wikipedia

    en.wikipedia.org/wiki/Laplace_equation_for_ir...

    And then using the continuity equation =, the scalar potential can be substituted back in to find Laplace's Equation for irrotational flow: ∇ 2 ϕ = 0 {\displaystyle \nabla ^{2}\phi =0\,} Note that the Laplace equation is a well-studied linear partial differential equation.

  7. Kutta–Joukowski theorem - Wikipedia

    en.wikipedia.org/wiki/Kutta–Joukowski_theorem

    In deriving the Kutta–Joukowski theorem, the assumption of irrotational flow was used. When there are free vortices outside of the body, as may be the case for a large number of unsteady flows, the flow is rotational. When the flow is rotational, more complicated theories should be used to derive the lift forces.

  8. Bernoulli's principle - Wikipedia

    en.wikipedia.org/wiki/Bernoulli's_principle

    If the fluid flow is irrotational, the total pressure is uniform and Bernoulli's principle can be summarized as "total pressure is constant everywhere in the fluid flow". [1]: Equation 3.12 It is reasonable to assume that irrotational flow exists in any situation where a large body of fluid is flowing past a solid body. Examples are aircraft in ...

  9. Velocity potential - Wikipedia

    en.wikipedia.org/wiki/Velocity_potential

    A velocity potential is a scalar potential used in potential flow theory. It was introduced by Joseph-Louis Lagrange in 1788. [1] It is used in continuum mechanics, when a continuum occupies a simply-connected region and is irrotational. In such a case, =, where u denotes the flow velocity.